Test Corrections and Retakes: These will only be offered if ALL homework from a unit is completed. Test corrections and retakes are offered until the next chapter/unit test or assessment.
DO YOU HAVE AN IPOD TOUCH? NEED A GRAPHING CALCULATOR? You can download a FREE graphing calculator app from iTunes. Free Graphing Calculator App
St. Cloud Math Contest April 7, 2011
St. Cloud State Math Contest:http://web.stcloudstate.edu/mathcontest/
The link will take you to some sample tests from past years. Below you will find some of the solutions to select questions from those tests.
For Solutions, see the links below. Keep in mind, these are not official answers, and if you disagree, let's have a discussion. Also, not all problems are completed. Bring any that you solve to me to check over your reasoning if I do not have a solution on my paper. 2009 SCSU math test.pdf 2010 SCSU math test.pdf
Monday 5/9/2011 - Friday 5/13/2011 Graphing Trig Functions We spent the week exploring how to graph Trig Functions in both degrees and radians. Basic Graphs: y = sin (x) Degrees Radians
Thursday 4/28/2011 Using the Unit Circle to find Trig Values sin = y cos = x tan = y/x If you know (x, y) for an angle from the unit circle, you know the exact value of the trig function.
FINISH HW5 for Monday!
Wednesday 4/27/2011 Trig Values for Any Angle We can use the terminal side of the angle to create a right triangle anywhere in the unit circle. The reference angles are then the "theta" that we base the trig ratios on. Pay attention to whether x and y are positive or negative for the terminal side. tan = sin / cos = y / x
HW5 #17-23
Tuesday 4/26/2011 Coterminal and Reference Angles Coterminal Angles: End in the same spot on the unit circle. Reference Angles: The acute angle between the x-axis and the terminal side of the angle. Ask: Which way is the shortest to the x-axis?
Monday 4/25/2011 Solving Right Triangles SOH CAH TOA is our trick for remembering the basic trig functions. Sine and CoSecant are reciprocals. Cosine and Secant are reciprocals. Tangent and Cotangent are reciprocals. Triangle Points Project:
Binomial Formula. Suppose a binomial experiment consists of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:
P = nCx * Px * (1 - P)n - x
Normal Distribution: Things that are normally distributed can have their probabilities predicted based on how far they are from the mean.
68% of the data is within one standard deviation on either side of the mean
95% is within 2 standard deviations on either side of the mean
99% is within 3 standard deviations on either side of the mean
3/25/2011- 3/29/2011 Probabililty Principles Addition and Independent Events OR- Add probabilities for each event AND- Multiply probabilities for each event HW2 due 3/30/2011
Dependent Events P(B|A) - the probability of event B based on A happening. How many options are there for A? This becomes the bottom of the fraction. Dependent Events Activity:
Tuesday 3/22/2011-Thursday 3/24/2011 Permutations and Combinations Permutations: used when the order of an arrangement matters nPr = n!/ (n - r)! Combinations: Used when the order of an arrangement does not matter. You are simply making a group of items. nCr = n! / (r! (n-r)!)
Monday 2/07/2011-Tuesday 2/08/2011: Radical Expressions Domain: Radical equations (with a square root sign) are only defined for postive numbers. Use an inequality to find the domain. Everything under the root must be >0. *REMEMBER: flip the inequality sign if you multiply or divide by a negative number.
*REMEMBER to use PEMDAS! Simplify the expression down to one number. The number on the outside of the root (index) tells you how many times a factor must appear to come out of the root. 1.) Factor the expression under the root. Use the index as a clue for what types of factors you want. 2.) Pull out factors that appear the correct number of times (2 for a square root, 3 for a cubed root, etc.) Review how to simplify square roots: Simplifying Square Roots
Graphing: What is the basic shape of a radical?
graph of sqare root of x
Use a table to find values for an equation. Remember all graphs should have this basic shape. HW12 due 2/11/2011
Thursday 2/03/2011: Solving Rational Equations 1.) Find a common denominator and simplify to one fraction on both sides of the =. 2.) Cross Multiply. The denominators will cancel, so the numerators are equal to each other. 3.) Solve for x. 4.) Check your solutions. Do they give an error in the denominator? HW11 due 2/09/2011
Monday 1/24/2011: Multiplying and Dividing Rational Functions 1.) Factor the numerators and denominators of all expressions. 2.) Cancel any groups which are the same on the top and bottom. 3.) Multiply across to simplify.
*If you are dividing, you must flip the second fraction (reciprocal) and multiply. Adding and Subtracting Rational Functions 1.) Make both functions have a common denominator. 2.) Multiply or distribute in each numerator. 3.) Combine like terms in the numerators. The denominator remains the same. *Watch for signs when you are subtracting the second rational. Change it to an addition problem before carrying out any operations.
Thursday 1/20/2011: Graphing Rational Functions 1.) Factor the top and bottom of the function. 2.) Find the holes. If something on the bottom cancels with something on the top, it creates a hole in the graph at the x-value that makes it a zero. 3.) Find the vertical asymptotes. Any groups left on the bottom should be set to zero. Find the x-values which make zero in the denominator. 4.) Find the horizontal asymptotes. Use table below to compare the degrees of the first terms. 5.) Draw in the asypmptotes on the graph. Use a calculator to find the basic shape of the curve around the asymptotes.
Tuesday 1/18/2011: Inverse and Joint Variation 1.) Find k (the constant of variation) 2.) Plug k in to the standard formula and find the missing value for the information given.
Inverse Variation: y = k/x (division) Joint Variation: z = kxy (multiplication) HW8 due 1/20/2011
Monday 1/10/2011: Finding the Zeros of a Polynomial
Steps for Finding Zeros:
1.) Factor the Polynomial so each term is in the form (ax + b) (use factoring, graphs, and division to find the factors)
2.) Set each factor equal to 0 and solve for x. ax + b = 0
Remember: There are the same number of roots as the degree of the polynomial (highest power).
Monday 1/03/2011: Intro to Polynomials Graphing Calculator will help you to find minimums and maximums. The standard form of a polynomial is to list terms from highest degree to lowest. We call the highest power the degree of the polynomial. Homework 5 due 1/06/2011
New Procedures:
Test Corrections and Retakes: These will only be offered if ALL homework from a unit is completed. Test corrections and retakes are offered until the next chapter/unit test or assessment.
Final Tests
2nd Period: Thursday, June 9th
7th Period: Wednesday, June 8th
Final Review Key:NOTES SHEET:
DO YOU HAVE AN IPOD TOUCH? NEED A GRAPHING CALCULATOR? You can download a FREE graphing calculator app from iTunes. Free Graphing Calculator App
St. Cloud Math Contest April 7, 2011
St. Cloud State Math Contest: http://web.stcloudstate.edu/mathcontest/The link will take you to some sample tests from past years. Below you will find some of the solutions to select questions from those tests.
For Solutions, see the links below. Keep in mind, these are not official answers, and if you disagree, let's have a discussion. Also, not all problems are completed. Bring any that you solve to me to check over your reasoning if I do not have a solution on my paper.
2009 SCSU math test.pdf
2010 SCSU math test.pdf
Trigonometry Identities Chapter 14
Test Thursday June 2nd
Review:
Algebra II Trig Review 14.4-14.6.doc
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Review Key:
Review Key.pdf
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- 86 KB
14.5C Solving Trig Functions
14.5 C Key:
14-5 Key.pdf
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- 54 KB
HW9 Sum and Difference, Double and Half Angle Formulas:
HW9 Sum and Difference Identities.doc
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- 48 KB
HW9 Key:
HW9 Key.pdf
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- 111 KB
HW8 Basic Trig Identities:
HW8 Basic Trig Identities.doc
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- 51 KB
HW8 Key:Trigonometry Basic Functions Chapter 13
Part 2 Test Tuesday 5/17/2011 (7th Period) Wednesday 5/18/2011 (2nd Period)
Chapter 13 Part 2 Review Key:Graphing Assignment 13.6B Answer Key:
Monday 5/9/2011 - Friday 5/13/2011 Graphing Trig Functions
We spent the week exploring how to graph Trig Functions in both degrees and radians.
Basic Graphs: y = sin (x)
Degrees Radians
y = cos (x)
Degrees Radians
Graphing Notes:
Explore how parameters change a basic graph (shifts, amplitude, and period): http://illuminations.nctm.org/ActivityDetail.aspx?id=174
HW7 due 5/16/2011:
HOMEWORK 7 KEY:
Friday 5/6/2011 Converting Radians to Degrees
Radians Notes:
Front of HW6 due 5/9/2011
Test: Tuesday 5/3/2011 (7th Period) Thursday 5/5/2011 (2nd Period)
Test Review Key:
13.1-13.3 Review Key.pdf
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UNIT CIRCLE (blank):
Thursday 4/28/2011 Using the Unit Circle to find Trig Values
sin = y
cos = x
tan = y/x
If you know (x, y) for an angle from the unit circle, you know the exact value of the trig function.
FINISH HW5 for Monday!
Wednesday 4/27/2011 Trig Values for Any Angle
We can use the terminal side of the angle to create a right triangle anywhere in the unit circle. The reference angles are then the "theta" that we base the trig ratios on. Pay attention to whether x and y are positive or negative for the terminal side.
tan = sin / cos = y / x
HW5 #17-23
Tuesday 4/26/2011 Coterminal and Reference Angles
Coterminal Angles: End in the same spot on the unit circle.
Reference Angles: The acute angle between the x-axis and the terminal side of the angle. Ask: Which way is the shortest to the x-axis?
HW 5 due Monday 4/2/2011
HW 5 KEY:
Monday 4/25/2011 Solving Right Triangles
SOH CAH TOA is our trick for remembering the basic trig functions.
Sine and CoSecant are reciprocals.
Cosine and Secant are reciprocals.
Tangent and Cotangent are reciprocals.
Triangle Points Project:
You need to collect 20 points. Solving triangles are 2 points a piece. Word problems are 4 points a piece. You must do at least one word problem.
==
Statistics Chapter 12==
Test Tuesday 4/19/2011
Blank Study GuideStudy Guide Key:
Thursday 4/14/2011
12.5-12.6 Binomial and Normal Distribution
HOMEWORK 4 KEY:
HW 4 Key Front.pdf
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HW 4 Key Back.pdf
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- 26 KB
Binomial Formula. Suppose a binomial experiment consists of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:
P = nCx * Px * (1 - P)n - x
Normal Distribution: Things that are normally distributed can have their probabilities predicted based on how far they are from the mean.
68% of the data is within one standard deviation on either side of the mean95% is within 2 standard deviations on either side of the mean
99% is within 3 standard deviations on either side of the mean
HW 4 due 4/19/2011
HW4 Binomial and Normal Distribution.doc
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Monday 4/11/2011
12.4 Measures of DispersionMean Deviation: The average distance from the mean.
Variance and Standard Deviation: Other measures of how far the average point is from the mean value.
Use your calculator.
HW 3 Measures of Dispersion due 4/15/2011
HW3 Measures of Deviation.doc
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- 46 KB
Probability and Counting Principles
Test Wednesday 3/30/2011
Study Guide Key
Chapter 10 Study Guide Key.doc
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- 8 MB
Chapter 10 Notes
CHapter 10 Notes Filled in.doc
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- 1 MB
Deck of Cards and Dice Model
Deck of cards.doc
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- 330 KB
3/25/2011- 3/29/2011 Probabililty PrinciplesAddition and Independent Events
OR- Add probabilities for each event
AND- Multiply probabilities for each event
HW2 due 3/30/2011
Dependent Events
P(B|A) - the probability of event B based on A happening. How many options are there for A? This becomes the bottom of the fraction.
Dependent Events Activity:
Tuesday 3/22/2011-Thursday 3/24/2011
Permutations and Combinations
Permutations: used when the order of an arrangement matters nPr = n!/ (n - r)!
Combinations: Used when the order of an arrangement does not matter. You are simply making a group of items. nCr = n! / (r! (n-r)!)
Notes from 10.2-10.3
HW 1 due 3/25/2011
Chapter 10 Notes:
10.1 Fundamental Counting Principle and Theoretical Probability
Need more examples of the FCM? Go here: Fundamental Counting Principle Videos
Radicals Test Wednesday, February 16th
Review Key:Chapter 8 Radical Functions
Monday 2/07/2011-Tuesday 2/08/2011: Radical ExpressionsDomain: Radical equations (with a square root sign) are only defined for postive numbers.
Use an inequality to find the domain. Everything under the root must be >0.
*REMEMBER: flip the inequality sign if you multiply or divide by a negative number.
Evaluating Expressions:
Evaluating Expressions Key:
*REMEMBER to use PEMDAS!
Simplify the expression down to one number. The number on the outside of the root (index) tells you how many times a factor must appear to come out of the root.
1.) Factor the expression under the root. Use the index as a clue for what types of factors you want.
2.) Pull out factors that appear the correct number of times (2 for a square root, 3 for a cubed root, etc.)
Review how to simplify square roots: Simplifying Square Roots
Graphing: What is the basic shape of a radical?
Use a table to find values for an equation. Remember all graphs should have this basic shape.
HW12 due 2/11/2011
HW12 Key
Thursday 2/03/2011: Solving Rational Equations
1.) Find a common denominator and simplify to one fraction on both sides of the =.
2.) Cross Multiply. The denominators will cancel, so the numerators are equal to each other.
3.) Solve for x.
4.) Check your solutions. Do they give an error in the denominator?
HW11 due 2/09/2011
Chapter 8 Rational Functions
Test on Chapter 8: Tuesday 2/1/2011
Review Key:
Rational Expressions Review Key.doc
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- 8 MB
Monday 1/24/2011: Multiplying and Dividing Rational Functions1.) Factor the numerators and denominators of all expressions.
2.) Cancel any groups which are the same on the top and bottom.
3.) Multiply across to simplify.
*If you are dividing, you must flip the second fraction (reciprocal) and multiply.
Adding and Subtracting Rational Functions
1.) Make both functions have a common denominator.
2.) Multiply or distribute in each numerator.
3.) Combine like terms in the numerators. The denominator remains the same.
*Watch for signs when you are subtracting the second rational. Change it to an addition problem before carrying out any operations.
HW10 due Thursday 1/27/2011:
HOMEWORK 10 KEY:
Thursday 1/20/2011: Graphing Rational Functions
1.) Factor the top and bottom of the function.
2.) Find the holes. If something on the bottom cancels with something on the top, it creates a hole in the graph at the x-value that makes it a zero.
3.) Find the vertical asymptotes. Any groups left on the bottom should be set to zero. Find the x-values which make zero in the denominator.
4.) Find the horizontal asymptotes. Use table below to compare the degrees of the first terms.
5.) Draw in the asypmptotes on the graph. Use a calculator to find the basic shape of the curve around the asymptotes.
HW9 due Monday 1/24/2011
Tuesday 1/18/2011: Inverse and Joint Variation
1.) Find k (the constant of variation)
2.) Plug k in to the standard formula and find the missing value for the information given.
Inverse Variation: y = k/x (division) Joint Variation: z = kxy (multiplication)
HW8 due 1/20/2011
Chapter 7 Polynomials
Test on Chapter 7: Thursday 1/13
Polynomials Review KeyMonday 1/10/2011: Finding the Zeros of a Polynomial
Steps for Finding Zeros:
1.) Factor the Polynomial so each term is in the form (ax + b) (use factoring, graphs, and division to find the factors)
2.) Set each factor equal to 0 and solve for x. ax + b = 0
Remember: There are the same number of roots as the degree of the polynomial (highest power).
Homework 7 due 1/12
HW 7 KEY :
Wednesday 1/05/2011: Mulitplying and Factoring Polynomials
There are several ways to factor polynomials:
HW 6 Multpilying and Dividing Polynomials
Monday 1/03/2011: Intro to Polynomials
Graphing Calculator will help you to find minimums and maximums.
The standard form of a polynomial is to list terms from highest degree to lowest. We call the highest power the degree of the polynomial.
Homework 5 due 1/06/2011